Question 541637: Mark and Kate are establishing a fund for their son's college education.What lump sum must they deposit in an account that gives 8% annual interest rate, compounded monthly, in order for them to have $60,000 in the fund art the end of 10 years?
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This is another example of the formula taught being correct, but less useful than a method or tool, that ought to be taught.
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The basic formula for relating present and future value of an investment is given by:
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FV = PV * (1 + r)^n
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where:
FV = Future Value
PV = Present Value
r = the interest rate (normally expressed as an annual rate)
n = number of periods for which the investment compounds (or the period number in question)
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Gotcha's to watch for:
Often the interest rate, r, is an annual rate; however, the compounding period is monthly or quarterly. If the compounding period and interest rate period are not the same, they need to adjusted. For example, in this case, we are given 8.00% annual rate, yet the investment compounds monthly. The simple solution is to convert the annual interest rate into a monthly rate by dividing by 12
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Given:
FV = $60,000
r = 8.00%
duration is 10 yrs
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For our formula above, n is not given, but it can be calculated. The problem asks for an initial deposit that results in a FV of $60,000 in 10 years. Therefore, multiply 10 * 12 months in a year to get:
n = 120
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We have FV, but our problem wants PV, so we rewrite the basic formula by dividing both sides by the compounding term, (1 + r)^n:
FV = PV * (1 + r)^ n
PV = FV / (1 + r)^n
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Solve for PV:
PV = 60,000 / (1+.08)^120
PV = $27,031.41
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Cheers,
Lee
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PS the problem with doing these problems by formula is that if you want to change something, you have to recalculate the formula each and every time. It would be much better to set this up in a spreadsheet so you can vary the term, the interest rate, and the deposited amount to see who variations in these quantities affects your FV. However, that is not what was asked. If you want help doing that, please email me.
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